| /////////////////////////////////////////////////////////////////////////////////// |
| /// OpenGL Mathematics (glm.g-truc.net) |
| /// |
| /// Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net) |
| /// Permission is hereby granted, free of charge, to any person obtaining a copy |
| /// of this software and associated documentation files (the "Software"), to deal |
| /// in the Software without restriction, including without limitation the rights |
| /// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
| /// copies of the Software, and to permit persons to whom the Software is |
| /// furnished to do so, subject to the following conditions: |
| /// |
| /// The above copyright notice and this permission notice shall be included in |
| /// all copies or substantial portions of the Software. |
| /// |
| /// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
| /// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
| /// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
| /// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
| /// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
| /// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
| /// THE SOFTWARE. |
| /// |
| /// @ref gtc_quaternion |
| /// @file glm/gtc/quaternion.inl |
| /// @date 2009-05-21 / 2011-06-15 |
| /// @author Christophe Riccio |
| /////////////////////////////////////////////////////////////////////////////////// |
| |
| #include "../trigonometric.hpp" |
| #include "../geometric.hpp" |
| #include "../exponential.hpp" |
| #include <limits> |
| |
| namespace glm{ |
| namespace detail |
| { |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER GLM_CONSTEXPR length_t tquat<T, P>::length() const |
| { |
| return 4; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER tquat<T, P>::tquat() : |
| x(0), |
| y(0), |
| z(0), |
| w(1) |
| {} |
| |
| template <typename T, precision P> |
| template <typename U, precision Q> |
| GLM_FUNC_QUALIFIER tquat<T, P>::tquat |
| ( |
| tquat<U, Q> const & q |
| ) : |
| x(q.x), |
| y(q.y), |
| z(q.z), |
| w(q.w) |
| {} |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER tquat<T, P>::tquat |
| ( |
| T const & s, |
| tvec3<T, P> const & v |
| ) : |
| x(v.x), |
| y(v.y), |
| z(v.z), |
| w(s) |
| {} |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER tquat<T, P>::tquat |
| ( |
| T const & w, |
| T const & x, |
| T const & y, |
| T const & z |
| ) : |
| x(x), |
| y(y), |
| z(z), |
| w(w) |
| {} |
| |
| ////////////////////////////////////////////////////////////// |
| // tquat conversions |
| |
| //template <typename valType> |
| //GLM_FUNC_QUALIFIER tquat<valType>::tquat |
| //( |
| // valType const & pitch, |
| // valType const & yaw, |
| // valType const & roll |
| //) |
| //{ |
| // tvec3<valType> eulerAngle(pitch * valType(0.5), yaw * valType(0.5), roll * valType(0.5)); |
| // tvec3<valType> c = glm::cos(eulerAngle * valType(0.5)); |
| // tvec3<valType> s = glm::sin(eulerAngle * valType(0.5)); |
| // |
| // this->w = c.x * c.y * c.z + s.x * s.y * s.z; |
| // this->x = s.x * c.y * c.z - c.x * s.y * s.z; |
| // this->y = c.x * s.y * c.z + s.x * c.y * s.z; |
| // this->z = c.x * c.y * s.z - s.x * s.y * c.z; |
| //} |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER tquat<T, P>::tquat |
| ( |
| detail::tvec3<T, P> const & u, |
| detail::tvec3<T, P> const & v |
| ) |
| { |
| detail::tvec3<T, P> w = cross(u, v); |
| T Dot = detail::compute_dot<detail::tvec3, T, P>::call(u, v); |
| detail::tquat<T, P> q(T(1) + Dot, w.x, w.y, w.z); |
| |
| *this = normalize(q); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER tquat<T, P>::tquat |
| ( |
| tvec3<T, P> const & eulerAngle |
| ) |
| { |
| tvec3<T, P> c = glm::cos(eulerAngle * T(0.5)); |
| tvec3<T, P> s = glm::sin(eulerAngle * T(0.5)); |
| |
| this->w = c.x * c.y * c.z + s.x * s.y * s.z; |
| this->x = s.x * c.y * c.z - c.x * s.y * s.z; |
| this->y = c.x * s.y * c.z + s.x * c.y * s.z; |
| this->z = c.x * c.y * s.z - s.x * s.y * c.z; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER tquat<T, P>::tquat |
| ( |
| tmat3x3<T, P> const & m |
| ) |
| { |
| *this = quat_cast(m); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER tquat<T, P>::tquat |
| ( |
| tmat4x4<T, P> const & m |
| ) |
| { |
| *this = quat_cast(m); |
| } |
| |
| ////////////////////////////////////////////////////////////// |
| // tquat<T, P> accesses |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER T & tquat<T, P>::operator[] (length_t i) |
| { |
| assert(i >= 0 && i < this->length()); |
| return (&x)[i]; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER T const & tquat<T, P>::operator[] (length_t i) const |
| { |
| assert(i >= 0 && i < this->length()); |
| return (&x)[i]; |
| } |
| }//namespace detail |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> conjugate |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| return detail::tquat<T, P>(q.w, -q.x, -q.y, -q.z); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> inverse |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| return conjugate(q) / dot(q, q); |
| } |
| |
| namespace detail |
| { |
| ////////////////////////////////////////////////////////////// |
| // tquat<valType> operators |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator += |
| ( |
| tquat<T, P> const & q |
| ) |
| { |
| this->w += q.w; |
| this->x += q.x; |
| this->y += q.y; |
| this->z += q.z; |
| return *this; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator *= |
| ( |
| tquat<T, P> const & q |
| ) |
| { |
| tquat<T, P> const p(*this); |
| |
| this->w = p.w * q.w - p.x * q.x - p.y * q.y - p.z * q.z; |
| this->x = p.w * q.x + p.x * q.w + p.y * q.z - p.z * q.y; |
| this->y = p.w * q.y + p.y * q.w + p.z * q.x - p.x * q.z; |
| this->z = p.w * q.z + p.z * q.w + p.x * q.y - p.y * q.x; |
| return *this; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator *= |
| ( |
| T const & s |
| ) |
| { |
| this->w *= s; |
| this->x *= s; |
| this->y *= s; |
| this->z *= s; |
| return *this; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator /= |
| ( |
| T const & s |
| ) |
| { |
| this->w /= s; |
| this->x /= s; |
| this->y /= s; |
| this->z /= s; |
| return *this; |
| } |
| |
| ////////////////////////////////////////////////////////////// |
| // tquat<T, P> external functions |
| |
| template <typename T, precision P> |
| struct compute_dot<tquat, T, P> |
| { |
| static T call(tquat<T, P> const & x, tquat<T, P> const & y) |
| { |
| tvec4<T, P> tmp(x.x * y.x, x.y * y.y, x.z * y.z, x.w * y.w); |
| return (tmp.x + tmp.y) + (tmp.z + tmp.w); |
| } |
| }; |
| |
| ////////////////////////////////////////////////////////////// |
| // tquat<T, P> external operators |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> operator- |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| return detail::tquat<T, P>(-q.w, -q.x, -q.y, -q.z); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> operator+ |
| ( |
| detail::tquat<T, P> const & q, |
| detail::tquat<T, P> const & p |
| ) |
| { |
| return detail::tquat<T, P>(q) += p; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> operator* |
| ( |
| detail::tquat<T, P> const & q, |
| detail::tquat<T, P> const & p |
| ) |
| { |
| return detail::tquat<T, P>(q) *= p; |
| } |
| |
| // Transformation |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec3<T, P> operator* |
| ( |
| detail::tquat<T, P> const & q, |
| detail::tvec3<T, P> const & v |
| ) |
| { |
| T Two(2); |
| |
| detail::tvec3<T, P> uv, uuv; |
| detail::tvec3<T, P> QuatVector(q.x, q.y, q.z); |
| uv = glm::cross(QuatVector, v); |
| uuv = glm::cross(QuatVector, uv); |
| uv *= (Two * q.w); |
| uuv *= Two; |
| |
| return v + uv + uuv; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec3<T, P> operator* |
| ( |
| detail::tvec3<T, P> const & v, |
| detail::tquat<T, P> const & q |
| ) |
| { |
| return glm::inverse(q) * v; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<T, P> operator* |
| ( |
| detail::tquat<T, P> const & q, |
| detail::tvec4<T, P> const & v |
| ) |
| { |
| return detail::tvec4<T, P>(q * detail::tvec3<T, P>(v), v.w); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<T, P> operator* |
| ( |
| detail::tvec4<T, P> const & v, |
| detail::tquat<T, P> const & q |
| ) |
| { |
| return glm::inverse(q) * v; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> operator* |
| ( |
| detail::tquat<T, P> const & q, |
| T const & s |
| ) |
| { |
| return detail::tquat<T, P>( |
| q.w * s, q.x * s, q.y * s, q.z * s); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> operator* |
| ( |
| T const & s, |
| detail::tquat<T, P> const & q |
| ) |
| { |
| return q * s; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> operator/ |
| ( |
| detail::tquat<T, P> const & q, |
| T const & s |
| ) |
| { |
| return detail::tquat<T, P>( |
| q.w / s, q.x / s, q.y / s, q.z / s); |
| } |
| |
| ////////////////////////////////////// |
| // Boolean operators |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER bool operator== |
| ( |
| detail::tquat<T, P> const & q1, |
| detail::tquat<T, P> const & q2 |
| ) |
| { |
| return (q1.x == q2.x) && (q1.y == q2.y) && (q1.z == q2.z) && (q1.w == q2.w); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER bool operator!= |
| ( |
| detail::tquat<T, P> const & q1, |
| detail::tquat<T, P> const & q2 |
| ) |
| { |
| return (q1.x != q2.x) || (q1.y != q2.y) || (q1.z != q2.z) || (q1.w != q2.w); |
| } |
| |
| }//namespace detail |
| |
| //////////////////////////////////////////////////////// |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER T length |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| return glm::sqrt(dot(q, q)); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> normalize |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| T len = length(q); |
| if(len <= T(0)) // Problem |
| return detail::tquat<T, P>(1, 0, 0, 0); |
| T oneOverLen = T(1) / len; |
| return detail::tquat<T, P>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> cross |
| ( |
| detail::tquat<T, P> const & q1, |
| detail::tquat<T, P> const & q2 |
| ) |
| { |
| return detail::tquat<T, P>( |
| q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z, |
| q1.w * q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y, |
| q1.w * q2.y + q1.y * q2.w + q1.z * q2.x - q1.x * q2.z, |
| q1.w * q2.z + q1.z * q2.w + q1.x * q2.y - q1.y * q2.x); |
| } |
| /* |
| // (x * sin(1 - a) * angle / sin(angle)) + (y * sin(a) * angle / sin(angle)) |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> mix |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y, |
| T const & a |
| ) |
| { |
| if(a <= T(0)) return x; |
| if(a >= T(1)) return y; |
| |
| float fCos = dot(x, y); |
| detail::tquat<T, P> y2(y); //BUG!!! tquat<T, P> y2; |
| if(fCos < T(0)) |
| { |
| y2 = -y; |
| fCos = -fCos; |
| } |
| |
| //if(fCos > 1.0f) // problem |
| float k0, k1; |
| if(fCos > T(0.9999)) |
| { |
| k0 = T(1) - a; |
| k1 = T(0) + a; //BUG!!! 1.0f + a; |
| } |
| else |
| { |
| T fSin = sqrt(T(1) - fCos * fCos); |
| T fAngle = atan(fSin, fCos); |
| T fOneOverSin = static_cast<T>(1) / fSin; |
| k0 = sin((T(1) - a) * fAngle) * fOneOverSin; |
| k1 = sin((T(0) + a) * fAngle) * fOneOverSin; |
| } |
| |
| return detail::tquat<T, P>( |
| k0 * x.w + k1 * y2.w, |
| k0 * x.x + k1 * y2.x, |
| k0 * x.y + k1 * y2.y, |
| k0 * x.z + k1 * y2.z); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> mix2 |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y, |
| T const & a |
| ) |
| { |
| bool flip = false; |
| if(a <= static_cast<T>(0)) return x; |
| if(a >= static_cast<T>(1)) return y; |
| |
| T cos_t = dot(x, y); |
| if(cos_t < T(0)) |
| { |
| cos_t = -cos_t; |
| flip = true; |
| } |
| |
| T alpha(0), beta(0); |
| |
| if(T(1) - cos_t < 1e-7) |
| beta = static_cast<T>(1) - alpha; |
| else |
| { |
| T theta = acos(cos_t); |
| T sin_t = sin(theta); |
| beta = sin(theta * (T(1) - alpha)) / sin_t; |
| alpha = sin(alpha * theta) / sin_t; |
| } |
| |
| if(flip) |
| alpha = -alpha; |
| |
| return normalize(beta * x + alpha * y); |
| } |
| */ |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> mix |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y, |
| T const & a |
| ) |
| { |
| T cosTheta = dot(x, y); |
| |
| // Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator |
| if(cosTheta > T(1) - epsilon<T>()) |
| { |
| // Linear interpolation |
| return detail::tquat<T, P>( |
| mix(x.w, y.w, a), |
| mix(x.x, y.x, a), |
| mix(x.y, y.y, a), |
| mix(x.z, y.z, a)); |
| } |
| else |
| { |
| // Essential Mathematics, page 467 |
| T angle = acos(cosTheta); |
| return (sin((T(1) - a) * angle) * x + sin(a * angle) * y) / sin(angle); |
| } |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> lerp |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y, |
| T const & a |
| ) |
| { |
| // Lerp is only defined in [0, 1] |
| assert(a >= static_cast<T>(0)); |
| assert(a <= static_cast<T>(1)); |
| |
| return x * (T(1) - a) + (y * a); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> slerp |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y, |
| T const & a |
| ) |
| { |
| detail::tquat<T, P> z = y; |
| |
| T cosTheta = dot(x, y); |
| |
| // If cosTheta < 0, the interpolation will take the long way around the sphere. |
| // To fix this, one quat must be negated. |
| if (cosTheta < T(0)) |
| { |
| z = -y; |
| cosTheta = -cosTheta; |
| } |
| |
| // Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator |
| if(cosTheta > T(1) - epsilon<T>()) |
| { |
| // Linear interpolation |
| return detail::tquat<T, P>( |
| mix(x.w, y.w, a), |
| mix(x.x, y.x, a), |
| mix(x.y, y.y, a), |
| mix(x.z, y.z, a)); |
| } |
| else |
| { |
| // Essential Mathematics, page 467 |
| T angle = acos(cosTheta); |
| return (sin((T(1) - a) * angle) * x + sin(a * angle) * z) / sin(angle); |
| } |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> rotate |
| ( |
| detail::tquat<T, P> const & q, |
| T const & angle, |
| detail::tvec3<T, P> const & v |
| ) |
| { |
| detail::tvec3<T, P> Tmp = v; |
| |
| // Axis of rotation must be normalised |
| T len = glm::length(Tmp); |
| if(abs(len - T(1)) > T(0.001)) |
| { |
| T oneOverLen = static_cast<T>(1) / len; |
| Tmp.x *= oneOverLen; |
| Tmp.y *= oneOverLen; |
| Tmp.z *= oneOverLen; |
| } |
| |
| #ifdef GLM_FORCE_RADIANS |
| T const AngleRad(angle); |
| #else |
| # pragma message("GLM: rotate function taking degrees as a parameter is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.") |
| T const AngleRad = radians(angle); |
| #endif |
| T const Sin = sin(AngleRad * T(0.5)); |
| |
| return q * detail::tquat<T, P>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin); |
| //return gtc::quaternion::cross(q, detail::tquat<T, P>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin)); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec3<T, P> eulerAngles |
| ( |
| detail::tquat<T, P> const & x |
| ) |
| { |
| return detail::tvec3<T, P>(pitch(x), yaw(x), roll(x)); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER T roll |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| #ifdef GLM_FORCE_RADIANS |
| return T(atan(T(2) * (q.x * q.y + q.w * q.z), q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z)); |
| #else |
| # pragma message("GLM: roll function returning degrees is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.") |
| return glm::degrees(atan(T(2) * (q.x * q.y + q.w * q.z), q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z)); |
| #endif |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER T pitch |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| #ifdef GLM_FORCE_RADIANS |
| return T(atan(T(2) * (q.y * q.z + q.w * q.x), q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z)); |
| #else |
| # pragma message("GLM: pitch function returning degrees is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.") |
| return glm::degrees(atan(T(2) * (q.y * q.z + q.w * q.x), q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z)); |
| #endif |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER T yaw |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| #ifdef GLM_FORCE_RADIANS |
| return asin(T(-2) * (q.x * q.z - q.w * q.y)); |
| #else |
| # pragma message("GLM: yaw function returning degrees is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.") |
| return glm::degrees(asin(T(-2) * (q.x * q.z - q.w * q.y))); |
| #endif |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tmat3x3<T, P> mat3_cast |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| detail::tmat3x3<T, P> Result(T(1)); |
| T qxx(q.x * q.x); |
| T qyy(q.y * q.y); |
| T qzz(q.z * q.z); |
| T qxz(q.x * q.z); |
| T qxy(q.x * q.y); |
| T qyz(q.y * q.z); |
| T qwx(q.w * q.x); |
| T qwy(q.w * q.y); |
| T qwz(q.w * q.z); |
| |
| Result[0][0] = 1 - 2 * (qyy + qzz); |
| Result[0][1] = 2 * (qxy + qwz); |
| Result[0][2] = 2 * (qxz - qwy); |
| |
| Result[1][0] = 2 * (qxy - qwz); |
| Result[1][1] = 1 - 2 * (qxx + qzz); |
| Result[1][2] = 2 * (qyz + qwx); |
| |
| Result[2][0] = 2 * (qxz + qwy); |
| Result[2][1] = 2 * (qyz - qwx); |
| Result[2][2] = 1 - 2 * (qxx + qyy); |
| return Result; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tmat4x4<T, P> mat4_cast |
| ( |
| detail::tquat<T, P> const & q |
| ) |
| { |
| return detail::tmat4x4<T, P>(mat3_cast(q)); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> quat_cast |
| ( |
| detail::tmat3x3<T, P> const & m |
| ) |
| { |
| T fourXSquaredMinus1 = m[0][0] - m[1][1] - m[2][2]; |
| T fourYSquaredMinus1 = m[1][1] - m[0][0] - m[2][2]; |
| T fourZSquaredMinus1 = m[2][2] - m[0][0] - m[1][1]; |
| T fourWSquaredMinus1 = m[0][0] + m[1][1] + m[2][2]; |
| |
| int biggestIndex = 0; |
| T fourBiggestSquaredMinus1 = fourWSquaredMinus1; |
| if(fourXSquaredMinus1 > fourBiggestSquaredMinus1) |
| { |
| fourBiggestSquaredMinus1 = fourXSquaredMinus1; |
| biggestIndex = 1; |
| } |
| if(fourYSquaredMinus1 > fourBiggestSquaredMinus1) |
| { |
| fourBiggestSquaredMinus1 = fourYSquaredMinus1; |
| biggestIndex = 2; |
| } |
| if(fourZSquaredMinus1 > fourBiggestSquaredMinus1) |
| { |
| fourBiggestSquaredMinus1 = fourZSquaredMinus1; |
| biggestIndex = 3; |
| } |
| |
| T biggestVal = sqrt(fourBiggestSquaredMinus1 + T(1)) * T(0.5); |
| T mult = static_cast<T>(0.25) / biggestVal; |
| |
| detail::tquat<T, P> Result; |
| switch(biggestIndex) |
| { |
| case 0: |
| Result.w = biggestVal; |
| Result.x = (m[1][2] - m[2][1]) * mult; |
| Result.y = (m[2][0] - m[0][2]) * mult; |
| Result.z = (m[0][1] - m[1][0]) * mult; |
| break; |
| case 1: |
| Result.w = (m[1][2] - m[2][1]) * mult; |
| Result.x = biggestVal; |
| Result.y = (m[0][1] + m[1][0]) * mult; |
| Result.z = (m[2][0] + m[0][2]) * mult; |
| break; |
| case 2: |
| Result.w = (m[2][0] - m[0][2]) * mult; |
| Result.x = (m[0][1] + m[1][0]) * mult; |
| Result.y = biggestVal; |
| Result.z = (m[1][2] + m[2][1]) * mult; |
| break; |
| case 3: |
| Result.w = (m[0][1] - m[1][0]) * mult; |
| Result.x = (m[2][0] + m[0][2]) * mult; |
| Result.y = (m[1][2] + m[2][1]) * mult; |
| Result.z = biggestVal; |
| break; |
| |
| default: // Silence a -Wswitch-default warning in GCC. Should never actually get here. Assert is just for sanity. |
| assert(false); |
| break; |
| } |
| return Result; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> quat_cast |
| ( |
| detail::tmat4x4<T, P> const & m4 |
| ) |
| { |
| return quat_cast(detail::tmat3x3<T, P>(m4)); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER T angle |
| ( |
| detail::tquat<T, P> const & x |
| ) |
| { |
| #ifdef GLM_FORCE_RADIANS |
| return acos(x.w) * T(2); |
| #else |
| # pragma message("GLM: angle function returning degrees is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.") |
| return glm::degrees(acos(x.w) * T(2)); |
| #endif |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec3<T, P> axis |
| ( |
| detail::tquat<T, P> const & x |
| ) |
| { |
| T tmp1 = static_cast<T>(1) - x.w * x.w; |
| if(tmp1 <= static_cast<T>(0)) |
| return detail::tvec3<T, P>(0, 0, 1); |
| T tmp2 = static_cast<T>(1) / sqrt(tmp1); |
| return detail::tvec3<T, P>(x.x * tmp2, x.y * tmp2, x.z * tmp2); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tquat<T, P> angleAxis |
| ( |
| T const & angle, |
| detail::tvec3<T, P> const & v |
| ) |
| { |
| detail::tquat<T, P> result; |
| |
| #ifdef GLM_FORCE_RADIANS |
| T const a(angle); |
| #else |
| # pragma message("GLM: angleAxis function taking degrees as a parameter is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.") |
| T const a(glm::radians(angle)); |
| #endif |
| T s = glm::sin(a * T(0.5)); |
| |
| result.w = glm::cos(a * T(0.5)); |
| result.x = v.x * s; |
| result.y = v.y * s; |
| result.z = v.z * s; |
| return result; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<bool, P> lessThan |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y |
| ) |
| { |
| detail::tvec4<bool, P> Result; |
| for(length_t i = 0; i < x.length(); ++i) |
| Result[i] = x[i] < y[i]; |
| return Result; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<bool, P> lessThanEqual |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y |
| ) |
| { |
| detail::tvec4<bool, P> Result; |
| for(length_t i = 0; i < x.length(); ++i) |
| Result[i] = x[i] <= y[i]; |
| return Result; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<bool, P> greaterThan |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y |
| ) |
| { |
| detail::tvec4<bool, P> Result; |
| for(length_t i = 0; i < x.length(); ++i) |
| Result[i] = x[i] > y[i]; |
| return Result; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<bool, P> greaterThanEqual |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y |
| ) |
| { |
| detail::tvec4<bool, P> Result; |
| for(length_t i = 0; i < x.length(); ++i) |
| Result[i] = x[i] >= y[i]; |
| return Result; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<bool, P> equal |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y |
| ) |
| { |
| detail::tvec4<bool, P> Result; |
| for(length_t i = 0; i < x.length(); ++i) |
| Result[i] = x[i] == y[i]; |
| return Result; |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<bool, P> notEqual |
| ( |
| detail::tquat<T, P> const & x, |
| detail::tquat<T, P> const & y |
| ) |
| { |
| detail::tvec4<bool, P> Result; |
| for(length_t i = 0; i < x.length(); ++i) |
| Result[i] = x[i] != y[i]; |
| return Result; |
| } |
| }//namespace glm |